.. only:: html
.. note::
:class: sphx-glr-download-link-note
Click :ref:`here ` to download the full example code
.. rst-class:: sphx-glr-example-title
.. _sphx_glr_generated_examples_coordinates_rv-to-gsr.py:
================================================================
Convert a radial velocity to the Galactic Standard of Rest (GSR)
================================================================
Radial or line-of-sight velocities of sources are often reported in a
Heliocentric or Solar-system barycentric reference frame. A common
transformation incorporates the projection of the Sun's motion along the
line-of-sight to the target, hence transforming it to a Galactic rest frame
instead (sometimes referred to as the Galactic Standard of Rest, GSR). This
transformation depends on the assumptions about the orientation of the Galactic
frame relative to the bary- or Heliocentric frame. It also depends on the
assumed solar velocity vector. Here we'll demonstrate how to perform this
transformation using a sky position and barycentric radial-velocity.
*By: Adrian Price-Whelan*
*License: BSD*
Make print work the same in all versions of Python and import the required
Astropy packages:
.. code-block:: default
import astropy.units as u
import astropy.coordinates as coord
Use the latest convention for the Galactocentric coordinates
.. code-block:: default
coord.galactocentric_frame_defaults.set('latest')
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
For this example, let's work with the coordinates and barycentric radial
velocity of the star HD 155967, as obtained from
`Simbad `_:
.. code-block:: default
icrs = coord.ICRS(ra=258.58356362*u.deg, dec=14.55255619*u.deg,
radial_velocity=-16.1*u.km/u.s)
We next need to decide on the velocity of the Sun in the assumed GSR frame.
We'll use the same velocity vector as used in the
`~astropy.coordinates.Galactocentric` frame, and convert it to a
`~astropy.coordinates.CartesianRepresentation` object using the
``.to_cartesian()`` method of the
`~astropy.coordinates.CartesianDifferential` object ``galcen_v_sun``:
.. code-block:: default
v_sun = coord.Galactocentric().galcen_v_sun.to_cartesian()
We now need to get a unit vector in the assumed Galactic frame from the sky
position in the ICRS frame above. We'll use this unit vector to project the
solar velocity onto the line-of-sight:
.. code-block:: default
gal = icrs.transform_to(coord.Galactic)
cart_data = gal.data.to_cartesian()
unit_vector = cart_data / cart_data.norm()
Now we project the solar velocity using this unit vector:
.. code-block:: default
v_proj = v_sun.dot(unit_vector)
Finally, we add the projection of the solar velocity to the radial velocity
to get a GSR radial velocity:
.. code-block:: default
rv_gsr = icrs.radial_velocity + v_proj
print(rv_gsr)
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
123.3046008737976 km / s
We could wrap this in a function so we can control the solar velocity and
re-use the above code:
.. code-block:: default
def rv_to_gsr(c, v_sun=None):
"""Transform a barycentric radial velocity to the Galactic Standard of Rest
(GSR).
The input radial velocity must be passed in as a
Parameters
----------
c : `~astropy.coordinates.BaseCoordinateFrame` subclass instance
The radial velocity, associated with a sky coordinates, to be
transformed.
v_sun : `~astropy.units.Quantity`, optional
The 3D velocity of the solar system barycenter in the GSR frame.
Defaults to the same solar motion as in the
`~astropy.coordinates.Galactocentric` frame.
Returns
-------
v_gsr : `~astropy.units.Quantity`
The input radial velocity transformed to a GSR frame.
"""
if v_sun is None:
v_sun = coord.Galactocentric().galcen_v_sun.to_cartesian()
gal = c.transform_to(coord.Galactic)
cart_data = gal.data.to_cartesian()
unit_vector = cart_data / cart_data.norm()
v_proj = v_sun.dot(unit_vector)
return c.radial_velocity + v_proj
rv_gsr = rv_to_gsr(icrs)
print(rv_gsr)
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
123.3046008737976 km / s
.. rst-class:: sphx-glr-timing
**Total running time of the script:** ( 0 minutes 0.022 seconds)
.. _sphx_glr_download_generated_examples_coordinates_rv-to-gsr.py:
.. only :: html
.. container:: sphx-glr-footer
:class: sphx-glr-footer-example
.. container:: sphx-glr-download sphx-glr-download-python
:download:`Download Python source code: rv-to-gsr.py `
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: rv-to-gsr.ipynb `
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery `_